Wave filter

ABSTRACT

531,662. Impedance networks. STANDARD TELEPHONES &amp; CABLES, Ltd. July 28, 1939, Nos. 21991, 21992 and 21993. Convention dates, July 28, 1938, Sept. 20, 1938, and Sept. 28, 1938. [Class 40 (iii)] In an unbalanced wave filter of the bridged-T type (which may degenerate into one of pi type), the series arms of the T comprise a single crystal having a split electrode on one or each side. Attenuation peaks may be located at any distance from the pass range, the number of such peaks may be increased by the addition of further crystals, and inherently high or low image impedances may be attained by the use of shunt or series terminal inductances. In the arrangement shown in Fig. 1, the series arms comprise the impedances between the part electrodes 5, 7 and 6, 8 respectively, together with shunt condensers C 1 . The bridging arm Z 1  and shunt arm Z 2  may have various forms, and the lower terminals 2, 4 may be earthed. The Specification gives the lattice network, Fig. 3 (not shown) equivalent to that shown in Fig. 1, and deduces the transmission characteristics of the filter. In a band-pass filter, Figs. 4 to 7 (not shown), the bridging arm Z 1  may be a capacitance while Z 2  is replaced by a direct connection ; the band-width can be increased by reducing the capacitance C 1  shunting the crystal, while the frequency of an attenuation peak below the pass band can be adjusted by varying the capacitance which forms the bridging arm Z 1 . The attenuation peak is located above the pass band if the poling of the part-electrodes 6, 8 is reversed, so that the electrodes shall be cross-connected, Figs. 8 to 11 (not shown). Attenuation peaks on both sides of the band can be obtained by connecting filters of the two types in cascade, Fig. 12 (not shown), their impedances being matched and their transmission bands identical. For a pass band of maximum width, the capacitances C 1  are omitted, so that the network consists of the crystal X with a bridging condenser at Z,. For a low-pass filter, Figs. 13 to 18 (not shown), the bridging arm Z 1  may be a parallel-tuned circuit while the shunt arm Z, is replaced by a direct connection. In a band-stop filter, with two attenuation peaks in the stop band, Figs. 19 to 22 (not shown), the bridging arm Z, is a parallel-resonant arm while the shunt arm Z 2  is an inductance. Fig. 23 shows a high-pass filter, in which the bridging arm Z, comprises a series resonant arm L 4 , C 9  which may be shunted by a capacitance C 10 , while the shunt arm Z 2  comprises an inductance ; and the former arm may be replaced by a crystal X, equivalent to it, Fig. 27. In another high-pass filter, Fig. 20, and Figs. 29 to 31 (not shown), the electrodes of the crystal X are reversely poled, the bridging arm Z, is a capacitance, and the shunt arm Z, is a series resonant circuit. In a band-pass filter with two attenuation peaks, Fig. 31 (and Figs. 32 to 35, not shown) the crystal X is crossconnected and is paralleled by a tee comprising a pair of inductances 4a which give the network a high-image impedance, in series with an adjustable resistance R 3 . The inductances La have a series-opposing mutual inductance. The bridging arm Z, is a capacitance which can be adjusted to vary the location of the peaks of attenuation ; and this adjustment can also be effected by adjusting the coupling of the inductances La. In the absence of such coupling one of the peaks is at zero frequency. The input and output terminals are shunted by capacitances C, which can be varied to vary the band-width. Instead of being cross-connected, the electrodes in Fig. 31 may be symmetrically connected as in Fig. 23 ; the circuit of Fig. 31 thus modified, Figs. 36, 37 (not shown) forms a band-pass filter with two attenuator peaks below the pass band ; the coupling between the inductances La may in this case be series-aiding or absent. The resistance R 5  may be replaced by a direct connection, while the capacity in the bridging arm Z, is shunted by an adjustable resistance, Figs. 30 to 41 (not shown) ; and such a shunt resistance may be used in the filters described above to compensate for dissipation in the inductances. A low image impedance is obtained by arranging inductances Lb, Fig. 42 (and Figs. 43 to 46, not shown), in series with the input and output terminals ; they may have a series-opposing mutual inductance, by decreasing which the frequency at which an attenuation peak occurs above the pass band may be raised; this peak is removed to infinite frequency when the mutual inductance falls to zero. If the crystal in Fig. 42 be cross-connected, Figs. 47, 48 (not shown), both attenuation peaks will lie above the pass band. Two crystals, X, X, Fig. 49 (and Figs. 50 to 52, not shown) may have their pairs of electrodes connected in parallel, one of the crystals having its electrodes cross connected as shown. Such a filter gives in general three attenuation peaks. To produce a high image impedance, the inductances La are connected in shunt instead of series with the input and output terminals, Figs. 53 to 56 (not shown).

' H. G. ocH

July s, 1941.

wAvE FILTER Filed July 28, 1938 4 Sheets-Sheet 1 ENCY l l IFREQu FIG. 7

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WAVE FILTER Filed July 28, 193e ATTENUATION ATTENuATloN 4 Sheets-Sheet 2 4 fe FREQUENCY FIG/4 FREQUENCY July 8 1941- H. G. ocH

WAVE FILTER med July 28, 1938 4 shee'ts-'sheet s l0 FREQUENCY FREQUENCY .FREQUENCY Y C N E U m R /F w F/G. z3

FIG. 24

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A 7mm/5y' July "s, 1941. A H, G, CCH 2,248,776

WAVE FILTER CofC-)scu INVENTOR H a. och' atented July 8, 1941 WAVE FILTER Henry G. Och, West Englewood, N. J., assigner to Bell Telephone Laboratories, IncorporatedNew York, N. Y., a corporation of New York Application `lilly 28, 1938, Serial No. 221,721

20 Claims.

This invention relates to selective wave transmission networks which use piezoelectric crystals as impedance elements and more particularly to unbalanced wave filters of the bridged-T type.

The principal object of the invention is to reduce the number of component elements required in unbalanced wave lters.

A feature of the invention is a filter of the bridged-T type in which the series arms of the T are constituted by a single piezoelectric crystal with divided electrodes.

It has been known'heretofore how to construct bridged-T wave filters employing piezoelectric crystals in the bridging branch and in the shunt branch, but in these filters the series arms of the T have consisted of a pair of reactance elements such as inductors or capacitors. In accordance with the present invention the series arms of the T are constituted by a single crystal element having a split electrode on one or both sides. The shunt branch of the T and the bridging branch may comprise inductors or capacitors, or a combination of these, and may include one or more additional crystals. Capacitors may be connected in shunt at the ends of the crystal. The component elements may bearranged and proportioned to provide wave iilters of the low-pass, high-pass, band-pass or band-elimination type.

The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawings, of which:

Fig. 1 shows the general configuration of the network of the invention;

Fig. 2 is a perspective view of the piezoelectric crystal element showing how the electrodes are placed;

Fig. 3 is an equivalent lattice-circuit for the network of Fig. 1;

Fig. 4 shows a band-pass lter in accordance with the invention;

Fig. 5 is an equivalent lattice for the iilter of Fig. 4;

Fig. 6 represents the reactance characteristics of the line and diagonal branches of the lattice of Fig. 5;

Figq is a typical attenuation characteristic for the lter of Fig. 4;

Fig. 8 shows the reversed poling for the connections to the electrodes of the crystal in the circuit of Fig. 4;

Figs. 9, 10, and l1 show respectively the equivalent lattice, the reactance characteristics for the ranches and a typical attenuation characteristic for the filter of Fig. 8;

Fig. 12 isa composite network comprising the filters of Figs. 4 and 8 connected in tandem;

Fig. 13 shows the invention embodied in a lowpass lter;

Fig. 14 is an equivalent lattice for the filter of Fig. 13;

Figs. 15 and 16 show respectively the reactance characteristics of the impedance branches and the attenuation characteristic for one distribution of the critical frequencies in the equivalent lattice of Fig. 14;

Figs. 17 and 18 show respectively the reactance characteristics of the branches and a typical attenuation characteristic for another distribution of the critical frequencies in the lattice of Fig. 14;

Fig. 19 is a band-elimination -iilter in accordance with the invention;

Figs. 20, 21 and 22 show respectively the equivalent lattice, the reactance characteristics of the impedance branches and a typical attenuation .characteristic for the ilter of Fig. 19;

acteristic for the filter of Fig. 23;

Fig. 27 shows an alternative structurefor the filter of Fig. 23 in which the bridging branch includes a piezoelectric crystal element;

Fig. 28 shows another alternative circuit for the high-pass lter; and

Figs. 29 and 30 show respectively the equivalent lattice and the reactance characteristics of the branches for the lter of Fig. 28.

Fig. 1 is a general schematic diagram of the circuit arrangement of the filters 0f the invention, which are of the bridged-T type. The series arms of the T are constituted by a piezoelectric crystal X having four electrodes, two of which are connected to one terminal of the shunt impedance branch Z2 and the remaining two of which are connected, respectively, to an input terminal I and the corresponding output terminal 3. 'Ihe bridging branch of the network is constituted by the impedance Z1. Two equal capacitors C1, C1, designated by their capacitances, are connected in shunt at the ends of the crystal. The impedances Z1 and Z2 may be of any degree of complexity and may comprise inductors, capacitors and additional crystals. Suitable load impedances may be connected to the input terminals l, 2 and the output terminals 3, 4. The ligure shows the unbalanced form of the network in which the path between terminals 2 and i may be grounded or otherwise fixed in potential. The lter may, of course, be built in the balanced form.

The crystal X is preferably of quartz in the form ofv a relatively narrow rectangular plate cut perpendicular to the electrical axis of the crystal and with its length in the direction ofthe mechanical axis. Such a crystal will vibrate longitudinally when alternating potentials are applied to electrodes placed on the larger surfaces. Other well-known types of crystal cut may be used and, under certain conditions, they may be preferred. The crystal shown in Fig. 1 is of the rectangular type described above but for convenience is shown in end elevation.

As shown in more detail in the perspective View of Fig 2, the crystal X is provided with two electrodes 5, 6 on one of the major faces and two oppositely disposed electrodes 1, 8 on the opposite face. These electrodes may be of silver, aluminum or `other suitable metal, plated directly onto the crystal, and may be applied by plating the two surfaces all over and afterwards removing a narrow longitudinal strip of the plating along the center of each face. It is generally desirable also to remove narrow strips of the plating around the edges of the crystal. When the crystal vibrates in the longitudinal mode, it is preferably supported between two or more opposymmetrical lattice network to which it is equiva' lent. The line branch of the equivalent lattice is equal to half of the impedance measured between termin-als I and 3 of Fig. l, and the diagonal branch is equal to twice the impedance measured between terminals I an-d 3 strapped together and terminal 2 or 4. It i-s apparent that the mechanical vibration of the crystal occurs for only one of these measurements, depending upon the poling of the crystal electrodes. Therefore, the impedance representing the piezoelectric properties of the crystal will appear in only one of the branches of the lattice. The electrode capacitance of the crystal, however, will appear in the other branch. Fig. 3 shows the equivalent lattice for the poling shown in Fig. 1, where the interconnected electrodes are on the same side' of the crystal. For this case the crystal impedance appears in the diagonal branch. The equivalent lattice comprises two similar line impedance branches Za each consisting of the electrode capacitance Cu, an impedance and the capacitance C1, all connected in parallel, and two similar 4diagonal impedance rbranches Zh each made up of an impedance 2Z2 in series with the crystal impedance, the latter being shunted by the capacitance C1. For the salie of clarity, in this and in subsequent iigures only one line branch and one diagonal branch are shown in detail, the other corresponding line and diagonal branches being indicated by dotted lines connect.. ing the appropriate terminals.

In Fig. 3 the crystal impedance is represented by its equivalent circuit comprising the capacitance C0 shunted by a branch consisting of an inductance L in series with a second capacitance C. The capacitance Co represents the simple electrostatic capacitance between a pair of oppositely disposed electrodes, such as 5 and 1. The values of the capacitance C and the inductance L depend upon'the dimensions of the crystal and also upon its piezoelectric and elastic constants. The values of the elements in the equivalent circuit for the crystal, in terms of the dimensions of the crystal X, may be determined from the following formulas, assuming that the electrodes cover substantially the entire area of the two major faces of the crystal.

in which Z, w and t are, respectively, the length, width and thickness of the crystal measured in centimeters. The remaining impedances in the lattice are the same as the corresponding ones in the bridged-T, multiplied by the numerical factors as indicated.

If reversed poling is used in Fig. l, that is, if the connections to a pair of oppositely disposed electrodes, for example electrodes 6 and 8, are interchanged, the impedance representing the piezoelectric properties of the crystal will appear in the line impedance branch instead of in the diagonal branch of the equivalent lattice. This means that in Fig. 3 the arm consisting of the capacitance C and the inductance L will be removed from the diagonal branch Zt and placed in parallel with the electrode capacitance Cn in the line branch Za. The other component elements of the lattice will remain unchanged.

The image impedance K of the lattice network of Fig. 3 is given by the expression K =1/Z.Zb (4) and the propagation constant P may be found from the expression The filter will have transmission bands in the regions where Zn and Zh are of opposite sign and will Ihave attenuation bands where Za and Zb are of the same sign, with peaks of attenuation occurring at the frequencies where Za and Zb are equal. By virtue of the equivalence pointed out above, these expressions also give .the impedance and propagation constant of the bridged-T network of Fig. 1. The values of the various circuit elements of the lattice, including the electrical elements equivalent to the crystal, can be found from the resonant and anti-resonant frequencies of t'he Za and Zh branches by a direct application of R. M. Fos'ters reactance theorem given in the Bell System Technical Journal, vol. III, No. 2, April 1924, pages 259 to 267. The values of the component el-ements in the bridged-T network of Fig. 1 are found by applying the numerical factors indicated. By a Iproper choice of component elements any one of a variety of filter characteristics may be obtained. Some specific examples in accordance with the invention will next be considered.

Fig. 4 is a schematic diagram showing a bandpass iilter. The series arms of the T are pro vided by the crystal X1 which has the capacitors C1, C1 shunting its ends. The capacitor C2 forms the bridging branch, and no additional shunt mpedance is required. The poling shown in Fig. l is used for the connections to the electrodes of the crystal and since the two electrodes l and 8 on one side of the crystal are connected together they may be replaced by a single electrode 9 as shown.

tanli -1-23:

The equivalent lattice, following Fig. 3, is given in Fig. 5. The line impedance branch is a capacitance equal to the sum of Co, C1 and 2C2, and the diagonal branch is made up of a capacitance equal to Co plus C1 shunted by an arm representing the piezoelectric properties of the crystal and consisting of the inductance L in series with the capacitance C. Fig. 6 represents the reactancefrequency characteristics of the line and diagonal branches of the lattice of Fig. 5. The reactance of the line branch Za is that of a simple capacitance and is given by the solid-line curve. The reactance of the diagonal branch Zb, shown by the dotted-line curve, exhibits a resonance at the frequency f2 and an anti-resonance at the frequency fs. The transmission band extends from f2 to fa because in this region the reactances Za and Zh are of opposite sign. At all other frequencies the filter will attenuate, since the reactances are of the same sign. At some frequency f1. on the lower side of the transmission band, the two curves cross, and a peak of attenuation will occur here. A typical attenuation characteristic is shown symbolically in Fig. 7.

The magnitude of the capacitance C1 shunting each end of the crystal does not aiect the frequency of resonance f2 but it does determine the location of the anti-resonance frequency f3. Since the width of the transmission band is determined by the separation of these two frequencies the band width of the filter can therefore be adjusted by varying the value of this capacitance. As indicated by the arrows in Fig. 4, the capacitors C1, C1 may be made Variable for this purpose. The widest band is obtained when these capacitances are Zero, that is, when they are omitted from the circuit. As these capacitances are increased in value, the width of the band is decreased, and a band as narrow as desired may be obtained.

The capacitance C2 has its greatest effect on the location of the crossing point of the two reactance characteristics. Since the location of this point determines theplacing of the peak of attenuation, the peak may be adjusted by varying the magnitude of this capacitance. As indicated, the capacitor C2 may be made variable to adjust the location of the peak. If C2 is omitted the peak is relegated to Zero frequency and as the value of C2 is increased the peak is made to approach the lower cut-olf frequency f2.

In order to place the peak of attenuation on he upper side of the transmission band, instead of on the lower side, it is only necessary to reverse the poling of the connections to the crystal, as shown by the circuit of Fig. 8. Here the diagonally opposite electrodes and 'l of the crystal X2 are connected together and to the path between terminals 2 and 4 of the network. 'I'he remaining electrodes and 8 are connected, respectively, to the terminals l and 3. The capacitors C4, C4 are connected in shunt at the ends of the crystal, and the capacitor C3 forms the bridging branch.

For this connection the line branch of the equivalent lattice, as shown in Fig. 9, comprises a capacitance equal to the sum of Cn, 2C3 and C4 shunted by an arm consisting of the inductance L in series with the capacitance C, and the diagonal branch is constituted by a capacitance equal to Co plus C4. The reactance kcharacteristics of the line branch Za and the diagonal branch Zt are given, respectively, by the solid-line curve and the dotted-line curve of Fig. 10. The attenuation characteristic, as shown in Fig. 11, has a transmission band extending from f4 to f5 in the region where the branch Za has a positive reactance, and an attenuation peak at the frequency f6, on the upper side of the pass band, where the curves cross. The capacitor C3 may be made variable to adjust the location of the attenuation peak and the end capacitors C4, C4 may be made variable to adjust the width of the transmission band.

An attenuation characteristic having a peak on each side of the transmission band can be obtained by connecting in tandem the lter of Fig. 4 and the filter `of Fig. 8. The filters should have matching image impedances and the same transmission band. Such a composite lter is shown in Fig. 12. The two capacitors C1and C4 connected in parallel at the junction of the two sections may, of course, be replaced by a single capacitance equal to the sum of the two.

1t will be noted that the band-pass filters shown in Figs. 4 and 8 require a minimum number of component reactance elements. If the full band width is used, so that the end capacitors may be omitted, each filter requires only a single crystal and one capacitor. No inductors are required in the design. The other filters described hereinafter are also very economical in their use of elements.

The network of Fig. 4 can be converted into a low-pass nlter by the addition of an inductance in the bridging branch, as shown in Fig. 13. The series arms of the T are provided by the crystal X3, which is shunted at its ends by the capacitors Cs and Cs. The bridging branch consists of the inductance L1 and a capacitance Cc connected in parallel. The equivalent lattice is given in Fig. 14 and the reactance characteristics of the line and diagonal branches are given in Fig. 15. The line branch is a simple anti-resonant circuit andthe diagonal branch has a resonance and an antiresonance. If the anti-resonance of the line branch is made to coincide with the resonance of the diagonal branch, at the frequency f7, the filter wiil freely transmit all frequencies lying below fs, the anti-resonance frequency of the diagonal branch. The attenuation characteristic for this distribution of the critical frequencies will be as shown symbolically in Fig. 16. An attenuation peak may be introduced by making the two anti-resonances coincide, at the frequency fa, as shown by the reactance characteristics of Fig. 17. The cut-oli will now occur at the frequency fs where the diagonal branch resonates, and the peak will be located at the frequency fio, where the curves cross. A typical attenuation characteristic is shown in Fig. 18.

The network of Fig. 13 can be converted into a band-elimination filter by the addition of an inductance L3 in the shunt arm of the T, as shown in Fig. 19. The crystal X4 provides the series arms of the T and the capacitors Cs, Ca furnish the shunt capacitances. The bridging branch consists of the inductance L2 and the capacitance C7 connected in parallel. The equivalent lattice is shown in Fig. 20 and the reactance characteristics of the two branches are given in Fig. 21. An additional resonance is introduced into the diagonal branch Zb, at the frequency h5, and the attenuation band will extend from this frequency to the lower resonance at fu. The two anti-resonances are placed at the same frequency, fia, and the curves will ordinarily cross at two frequencies, such as f12 and f14, thus locating the peaks of attenuation as shown by the characteristic of Fig. 22'. If the two curves do not cross, the two peaks will coalesce and there will be a single peak located at the frequency of anti-resonance J13.

The network of Fig. 19 can be converted to a high-pass filter by arranging the inductance and the capacitance in the bridging branch in series instead of in parallel, as shown in Fig. 23 by the elements L4 and C9. A shunting capacitor, represented by Cio, is also sometimes required in the bridging branch. The equivalent lattice is shown in Fig. 24 and the reactance characteristics of the branches are given in Fig. 25. A resonance is introduced in the line branch, at the frequency fw, and the anti-resonance occurs at fm1. The anti-resonance of the diagonal branch is made to coincide with the resonance of the line branch, and the upper resonance of the diagonal branch is placed at the anti-resonance of the line branch. The lower resonance of the diagonal branch, occurring at fm, determines the cut-off of the filter. The curves can be made to cross at two frequencies, such as fm and fw, at which points there will be attenuation peaks. Fig. 26 gives a typical attenuation characteristic It is seen that the bridging branch Z1 of the filter of Fig. 23 has the same configuration as the equivalent electrical circuit for a crystal. In certain cases this branch can, therefore, be replaced by a crystal element Xs as shown in Fig. 27. 'I'he other elements in Fig. 27 are the same as those in Fig. 23, and the two networks can be designed to have identical attenuation characteristics.

Another form of high-pass lter is shown in Fig. 28 in which the crystal X7 employs reversed poling and is shunted at its ends by the capacitors C13 and C13. The capacitor C12 forms the bridging branch, and the shunt branch is constituted by the capacitor C14 and the inductor Ls connected in series. The equivalent lattice is given in Fig. 29 and the reactance characteristics of its branches in Fig. 30. The line branch has a resonance at f2s, which determines the cutoff, and an anti-resonance at fzi which coincides with the resonance of the diagonal branch. The peaks of attenuation occur at the frequencies fzi and 322 where the two curves cross. The attenuation characteristic is of the same type as that shown in Fig. 26. It will be noted that this high-pass filter requires only one inductor and a single crystal element.

As already pointed out the general impedances Z1 and Z2 of Fig. 1 may have any degree of complexity. It follows, therefore, that one skilled in lter design may devise many other circuits in accordance with the principles of the invention set forth above. The circuits shown and described are to be considered merely as illustrative.

What is claimed is:

1. A wave filter of the bridged-T type having a pair of input terminals and a pair of output terminals, said lter comprising a piezoelectric crystal having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, two of said electrodes being connected directly together and through a common shunt branch to an input terminal and an associated output terminal, and the remaining electrodes being connected respectively to the remaining terminals, and a bridging impedance branch connected between said remaining terminals, the dimensions of said crystal and the values of the reactance elements forming said bridging branch and said shunt branch being` proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

2. A wave lter in accordance with claim 1 in which said bridging branch includes a capacitor.

3. A wave filter of the bridged-T type comprising a symmetrical T network consisting of two equal series arms and an interposed shunt impedance branch connected between a pair oi input terminals and a pair of output terminals, and a bridging impedance branch connected between the outer terminals of said series arms, said series arms being constituted by a single piezoelectric crystal having a divided electrode on at least one side, and the dimensions of said crystal and the values of the reactance elements constituting said bridging branch and said shunt branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

4. A Wave filter in accordance with claim 3 in which said shunt branch includes an inductor.

5. A wave filter in accordance with claim 3 in which said bridging branch includes a second piezoelectric crystal.

6. A wave lter in accordance with claim 3 which includes equal capacitors connected in shunt at the ends of said crystal.

'7. A wave filter in accordance with claim 3 in which said bridging branch includes a capacitor.

8. A wave filter in accordance with claim 3 in which said bridging branch includes a capacitor and an inductor connected in series and said shunt branch includes a second inductor.

9. A wave filter of the bridged-T type comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, and a piezoelectric crystal having two electrodes on one face and a third electrode on the opposite face, said two electrodes being connected respectively to the terminals of said bridging branch, said third electrode being connected to the remaining input terminal and output terminal, and the dimensions of said crystal and the values of the reactance elements constituting said bridging branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

10. A wave lter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, and a piezoelectric crystal having two electrodes on one face and two other electrodes on the opposite face, an electrode on one face and an electrode on the opposite face being connected respectively to the terminals of said bridging branch, the remaining electrodes being connected together and to the remaining input terminal and output terminal, and the dimensions of said crystal and the values of the reactance elements constituting said bridging branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

11. A wave filter having a pair of input terminals and a pair of output terminals, said filter comprising a piezoelectric crystal having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, two of said electrodes on the same face of the crystal being connected together and through a shunt branch to an input terminal and an associated output terminal and the remaining electrodes being connected respectively to the remaining terminals, and a bridging impedance branch connected between said remaining terminals, the dimensions of said crystal and the values of the reactance elements forming said bridging branch and said shunt branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

12. A wave filter having a pair of input terminals and a pair of output terminals, said filter comprising apiezoelectric crystal having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, two of said electrodes which are diagonally opposite to each other being connected together and through a shunt branch to an input terminal and an associated output terminal and the remaining electrodes being connected respectively to the remaining terminals, and a bridging impedance branch connected between said remaining terminals, the dimensions of said crystal and the values of the reactance elements forming said bridging branch and said shunt branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

13. A wave filter having a pair of input terminals and a pair of output terminals, said filter comprising a piezoelectric crystal having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, two of said electrodes being connected together and through a shunt branch to an input terminal and an associated output terminal and the remaining electrodes being connected respectively to the remaining terminals, a bridging impedance branch connected between said remaining terminals, and equal reactance elements connected in shunt at the ends of said crystal, the dimensions of said crystal and the values of said equal reactance elements and the reactance elements forming said bridging branch and said shunt branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies.

14. A wave filter in accordance with claim 13 in which said equal reactance elements are capacitors.

15. A wave filter having a pair of input terminais and a pair of output terminals, said filter comprising a piezoelectric crystal having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, two of said electrodes being connected together and through a shunt branch to an input terminal and an associated output terminal and the remaining electrodes being connected respectively to the remaining terminals, and a bridging impedance branch including a capacitor and an inductor connected between said remaining terminals, the dimensions of said crystal and the values of the reactance elements forming said bridging branch and said shunt branch being proportioned with respect to one another and with respect to two preassgned frequencies 4to provide a transmission band between said frequencies.

16. A wave nlter in accordance with claim -15 in which said capacitor and inductor are connected in series.

17. A wave filter in accordance with claim 15 in which said capacitor and inductor are connected in parallel.

18. In combination, two wave filters connected in tandem, each of said filters having a vpair of input terminals and a pair of output terminals and each of said filters comprising a piezoelectric crystal having two electrodes on one face and two other oppositely disposed electrodes on the opposite face, two of said electrodes being connected together and through a shunt branch to an input terminal and an associated output terminal and the remaining electrodes being connected respectively to the remaining terminals, and a bridging impedance branch connected between said remaining terminals, the dimensions of said crystal and the values of the reactance elements forming said bridging branch and said shunt branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies, said lters having the same transmission band, the interconnected electrodes in one of said lters being on the same side of the crystal and the interconnected electrodes in the other of said filters being diagonally opposite to each other.

19. A wave lter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, and a piezoelectric crystal having two electrodes on one face and a third electrode on the opposite face, said two electrodes being connected respectively to the terminals of said bridging branch, said third electrode being connected to the remaining input terminal and output terminal, the dimensions of said crystal and the values of the reactance elements constituting said bridging branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies and said capacitor being made variable in order to adjust the location of a peak of attenuation in the attenuation characteristics of the lter.

20. A wave filter comprising a pair of input terminals, a pair of output terminals, a bridging impedance branch including a capacitor connected between an input terminal and a corresponding output terminal, a piezoelectric crystal having two electrodes on one face and a third electrode on the opposite face, and two equal capacitors, said two electrodes being connected respectively to the terminals of said bridging branch, said third electrode being connected to the remaining input terminal and output terminal, said equal capacitors being connected in shunt at the ends of said crystal, the dimensions of said crystal and the values of said equal capacitors and the reactance elements constituting said bridging branch being proportioned with respect to one another and with respect to two preassigned frequencies to provide a transmission band between said frequencies, and said equal capacitors being made variable in order to adjust the width of said transmission band.

HENRY G. OCI-I. 

